Theorems · Definition · category theory
CategoryTheory.InternallyProjective
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.MonoidalCategory C] → [CategoryTheory.MonoidalClosed C] → C → PropAn object P : C is internally projective if the functor P ⟶[C] - taking internal homs
out of P preserves epimorphisms.
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
- CategoryTheory.MonoidalClosedstatement and proof · cited by 134
- CategoryTheory.ObjectProperty.Isproof · cited by 4
- CategoryTheory.isInternallyProjectiveproof · cited by 2
Cited by8
Results whose statement or proof uses this declaration.
- LightCondensed.internallyProjective_iff_tensor_conditionstatement and proof · cited by 2
- LightCondensed.free_internallyProjective_iff_tensor_conditionstatement · cited by 1
- LightCondensed.free_internallyProjective_iff_tensor_condition'statement · cited by 1
- LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition'statement · cited by 1
- LightCondensed.internallyProjective_iff_tensor_condition'statement · cited by 1
- LightCondensed.internallyProjective_free_natUnionInftystatement · cited by 0
- LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_conditionstatement · cited by 0
- CategoryTheory.InternallyProjective.ofRetractstatement and proof · cited by 0